{
  "id": "2403.03513",
  "version": "v1",
  "published": "2024-03-06T07:40:53.000Z",
  "updated": "2024-03-06T07:40:53.000Z",
  "title": "Spectrum of random centrosymmetric matrices; CLT and Circular law",
  "authors": [
    "Indrajit Jana",
    "Sunita Rani"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We analyze the asymptotic fluctuations of linear eigenvalue statistics of random centrosymmetric matrices with i.i.d. entries. We prove that for a complex analytic test function, the centered and normalized linear eigenvalue statistics of random centrosymmetric matrices converge to a normal distribution. We find the exact expression of the variance of the limiting normal distribution via combinatorial arguments. Moreover, we also argue that the limiting spectral distribution of properly scaled centrosymmetric matrices follows the circular law.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-06T07:40:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "circular law",
      "random centrosymmetric matrices converge",
      "complex analytic test function",
      "normalized linear eigenvalue statistics",
      "limiting normal distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}